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You will also need to add DNS entries that correspond with the new server so that backup.yourdomain.com points to the IP address of your back-up mail server.

When the mail server at the IP address relating to mail.yourdomain.com is not available mail will be sent to backup.yourdomain.com

and then add the following line in /etc/mail/mailertable:

yourdomain.com smtp:mail.yourdomain.com

Next we need to add this to the mailertable database.
Type:
# makemap hash /etc/mail/mailertable.db < /etc/mail/mailertable
And then append the following lines to the bottom of your access file.
To:yourdomain.com RELAY
Now you should have something like this:
# by default we allow relaying from localhost...
localhost.localdomain RELAY
localhost RELAY
127.0.0.1 RELAY
To:yourdomain.com RELAY
now run:
makemap hash /etc/mail/access.db < /etc/mail/access
Now restart the sendmail service to make the changes complete
Type:
# service sendmail restart